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Topic: A possible paradox? (Read 489 times)

There are two important equations in the Theory of Relativity. One is the equation for figuring out spatial contraction, and the other is for figuring out time dilation. Now, according to the guy who gave a seminar at my college, from a photon's "perspective", everything appears to happen at the same time, and space is compressed to the point that, from its perspective, it travels from an arbitrary point A to an arbitrary point B in 0 seconds (instantaneously).Now, the Universe is in constant expansion. Assuming its expansion is speeding up[1], it will reach a point when the galaxies will drift apart from each other at speeds higher than light. In other words, light emitted from an arbitrary galaxy A will never reach galaxy B, no matter what. However, from a photon's perspective, it will still reach galaxy B, even though galaxy B keeps moving away at speeds higher than the photon can achieve (since, as you know, the speed of light is constant, regardless of the frame of reference). How is this possible? Is there something I'm missing?

A photon is at every point in its trajectory simultaneously, because it doesn't have mass (thus time doesn't exist for it). Meaning, it is at the starting point and the ending point of that trajectory at the same time. That doesn't mean it necessarily reaches galaxy B, though. It's limited to the actual trajectory it follows, so it can't go at right angles to galaxy C, for example. And that's your answer. If it never reaches galaxy B, then as far as the photon is concerned, galaxy B doesn't exist any more than galaxy C, D, E, F, and so on.

A photon is at every point in its trajectory simultaneously, because it doesn't have mass (thus time doesn't exist for it).<snip>

Two questions:1 - How does not having (rest) mass make it so time doesn't exist for it?2 - From whose perspective is it in every point in its trajectory simultaneously? I assume it's the photon's, but I want to be sure.

2. Yes, from the perspective of the photon. I answered this first because the answer to the first one is much more complicated.

1. Photons having a rest mass of zero[1] is a consequence of the theory of relativity, or at least that's my understanding. It's apparently necessary in order to bring them in line with the rest of the theory of relativity, since even though photons can't be brought to rest so we can actually measure their mass, treating them as if they have no rest mass gives the correct equation for the energy contained in light.

As for why it doesn't experience the passage of time, that's because time (and time contraction) is a consequence of having mass. Clocks near to gravity wells run slower than ones further away, just as clocks on something moving at relativistic speeds run slower that something not moving at those relativistic speeds. That's why scientists treat the mass of an object that's moving faster as higher than the same object at a slower relativistic speed. In short, greater mass = slower time, and lesser mass = faster time. But for a photon, which apparently doesn't have mass at all, it also doesn't experience time at all.

Basically, the less mass something has, the faster time passes for it. Another way of putting this is that the interval between units of time is directly proportionate to its mass, so if mass is less than 1, the time interval between units of time also becomes less than 1. As mass approaches 0, the time interval also approaches 0. Since we have to set the mass of light equal to 0 in order for general relativity to explain the behavior of light, that means that the time interval that light has must also be equal to 0, meaning that there's no difference between T = 1, T = 2, or T = 1000000000000000. To the photon, they all happen at the exact same time, because there's no interval to keep T = 2 from running into T = 1 - or to keep T = 1000000000000000 from running into T = 1 or T = 2 for that matter.

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You know, I'm beginning to wonder if this might not help explain the apparent expansion of the universe. If an increase in mass equates to a contraction of distance, then wouldn't a decrease in mass equate to a stretching of distance? If this is right, as things outside our frame of reference move away from us, their mass also decreases (as far as we're concerned), meaning that the apparent distance between us and them increases. It's like the opposite of the effect we get when we start moving at relativistic velocities towards another object - the distance between us and them contracts (which is why less time would show on the clock for someone traveling at relativistic velocities to reach Alpha Centauri than our clocks would show). So if we're moving at relativistic velocities away from another object, then presumably, the distance between us and them would expand.

My Mechanics teacher, who took a course in particle physics, said the fact that the photon has zero rest mass is a postulate of the theory of relativity. As you said, it's not possible to measure it, since photons never stop moving.